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A carton of $24$ bulbs contain $6$ defective bulbs. $1$ bulb is drawn at random. If the bulb selected is defective and it is not replaced and a second bulb is selected at random from the rest, then from the options given below, what is the probability that the second bulb is defective?

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523

34

524

35

answer is A.

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Detailed Solution

It is given that, a carton consists of

24

bulbs containing

6

defective bulb.
We have to find the probability that the bulb is not defective.
There is a total of

24

bulbs in which

6

are defective, that means,

24 − 6 = 18

are non-defective.
So, the total number of outcomes is

24

.
Let

A

be the event that the bulb is not defective. Then,

P (A) = N u m b e r of favourable outcomes T o t a l number of outcomes

= 1824

= 34

Obtain the probability that the

2 n d

bulb is defective.
If the selected bulb is defective and not replaced, then the number of defective bulbs left in a cartoon is

24 − 1 = 23

Out of which

5

are defective since

1

defective bulb is already drawn out.
Let

B

be the event that the

2 n d

bulb is defective. Then,

P (B) = N u m b e r of favourable outcomes T o t a l number of outcomes

= 523

The probability that the

2 n d

bulb is defective is

523

.
Hence option 1) is correct.

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